Thursday, April 24, 2008

Quantile regression and extreme hurricane winds

Coastal tropical cyclones (TCs) pose a serious threat to society and the economy. Strong winds, heavy rainfall, and storm surge kill people and destroy property. The destructive power of the most intense TCs can rival that of earthquakes. The rarity of intense TCs implies that empirical estimates of their return periods will be unreliable. Fortunately extreme value theory provides parametric models for rare events and a justification for extrapolating to intensity levels that are greater than what has been observed. We developed an extreme value model for US hurricane intensity based on the method of peaks over thresholds using data over the period 1899-2006 (Jagger and Elsner 2006) and showed how the models can be used to assess the probability of extremely intense hurricanes controlling for climate factors.

Quantile regression offers another way to model extreme TC events that has yet to be examined. Quantile regression, introduced by Koenker and Bassett (1978), extends the ordinary least squares regression model to conditional quantiles (e.g., 90th percentile) of the response variable. It can be considered a semi-parametric technique because it relies on non-parametric quantiles, but uses parameters to assess the relationship between the quantile and the covariates.

Ordinarily we think of parametric models as more informative, with nonparametric models useful for an initial look at the data. A parametric model involves more stringent assumptions, but it is usually a good idea to start with stronger assumptions and back off toward weaker assumptions when necessary. However, parametric models are generally more sensitive to outlying data points, which can be problematic for extreme value models. Also, with parametric models care must be given to the form of the distribution. A drawback of parametric models is that the parameters can be more difficult to interpret physically. It is this difficulty in interpreting the parameters of the extreme value models with respect to issues of climate's influence on TC activity that prompted the present work. It is our contention that extreme value models are valuable for quantifying the probability of high winds from TCs conditional on climate covariates, but that quantile regression can be quite useful as an exploratory tool.

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